Graphing Rational Functions

TopWe can show Rational Function with following form by f (t) = p(t) / q(t), where p (t) and q (t) are polynomial Functions where it is necessary the function q (t) should not zero.
Here the Domain of the function f (t) is a Set of values of ‘t’ where function q(t) is not zero. For Graphing rational functions it is necessary that we follow some steps. In first step, we have to find out the domain of function f (t) after that we find out vertical Asymptote and at last Vertical Asymptote of function. To understand how we graph a rational expression we take an example of rational function. So
f (x) = 1 / (x+ 3),
Now we have a rational function f (t) and we have to find out domain for that so to determine that we have to set denominator equals to zero,
Then x + 3 = 0,
x = -3,
So we can say that the domain of function is all real Numbers except negative 3.
Now we have to find vertical asymptote of function f (t) so which x = -3 and at last we have to find Horizontal Asymptote and we can clearly see that the degree of numerator is zero which is less than in comparison of denominator. So vertical asymptote is
y = 0,
So now we can easily plot all other Point by putting the values of ‘x’ in the graph except x = -3. For example if we put the value x = -4.
Then y = 1 / (-4 + 3),
y = -1,
If we put the value x = -2 then in that case the value of ‘y’
y = 1/ (-2 + 3),
y = 1.
So like that we can easily find out the values of ‘y’ with respect to ‘x’ for function f(x).